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Showing 1 to 6 of 6 for “"Rational Homotopy Theory"”.
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Gröbner bases in rational homotopy theory
… Eckmann-Hilton dual that characterizes the homotopy of a pullback, but the Eilenberg-Moore spectral sequence has no dual that characterizes the homotopy of a pushout. The main obstacle is the lack of an Eckmann-Hilton dual to the Kiinneth theorem with which to understand the homotopy of a …
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On tautological classes of fibre bundles and self-embedding calculus
… generate. In the first part we use tools from rational homotopy theory to compute analogues of tautological rings over fibrations, which provides upper bounds on the tautological rings of fibre bundles. In some cases we find an upper bound on the Krull dimension that is sharp. In the second …
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On the higher Frobenius
Given a homotopy invariant of a space, one can ask how much of the space can be recovered from that invariant. This question was first addressed in work of Quillen and Sullivan on rational homotopy theory in the 1960's and in work of Dwyer-Hopkins and Mandell on p-adic homotopy theory in the …
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Derived mapping spaces as models for localizations by Jennifer E. French.
… focuses on a generalization of the models for rational homotopy theory developed by D. Sullivan and D. Quillen and p-adic homotopy developed by M. Mandell to K(1)-local homotopy theory. The work is divided into two parts. The first part is a reflection on M. Mandell's model for p-adic homotopy …
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Studying the Space of Almost Complex Structures on a Manifold Using de Rham Homotopy Theory
… result for such an invariant (the de Rham homotopy type) for each connected component of the space of cross-sections of certain fibrations. We then apply this result to differential geometry and prove a finiteness theorem of the de Rham homotopy type for each connected component of the …
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Cohomology Jumping Loci and the Relative Malcev Completion
Two standard invariants used to study the fundamental group of the complement X of a hyperplane arrangement are the Malcev completion of its fundamental group G and the cohomology groups of X with coefficients in rank one local systems. In this thesis, we develop a tool that unifies these two …